محاسبه‌ی میدان تنش مجانبی به همراه ضرایب شدت تنش و مرتبه بالاتر در شیار کلیدی‌شکل

نوع مقاله : مقاله علمی پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران

2 دانشگاه علم و صنعت ایران

چکیده

در پژوهش حاضر، ابتدا توزیع تنش مجانبی مود I بارگذاری با استفاده از روش توابع پتانسیل مختلط برای شیار‌های کلیدی‌شکل محاسبه شده‌است. سپس از روش فرامعین برای محاسبه‌ی ضرایب شدت تنش و ضرایب مرتبه بالاتر سری بدست آمده، استفاده می-شود. در پایان نیز برای ارزیابی صحت ضرایب محاسبه شده، میدان تنش حاصل از توزیع تنش مجانبی با مقادیر اجزا محدود مقایسه می-گردد. نتایج نشان می‌دهند که در نظر گرفتن ترم اول یا همان ترم تکین به تنهایی منجر به خطای زیادی در محاسبات می‌شود.

کلیدواژه‌ها

موضوعات


[1] Zappalorto, M., and Lazzarin, P., “In-plane and Out-of-plane Stress Field Solutions for V-notches with End Holes”, International Journal of Fracture, Vol. 168, No. 2, pp.167-180, (2011).
 
[2] Mori, K., “Tension of a Semi-infinite Plate with a Circular Hole Connected to the Straight Edge by a Slit. Bull”, J-STAGE, Vol. 7, No. 26, pp. 272-277, (1964).
 
[3] Neuber, H., “Theory of Notch Ntresses”, 2nd Edn., Springer, Berlin, (1958).
 
[4] Neuber, H., “Kerbspannungslehre”, 3rd Edn., Springer, Berlin, (1985).
 
[5] Kullmer, G., “Elastic Stress Fields in the Vicinity of a Narrow Notch with Circular Root. Reliability and Structural Integrity of Advanced Materials”, Proceedings of the 9th Biennial European Conference on Fracture (ECF 9), Vol. II., Varna, Bulgaria, pp. 905-910, (1992).
 
[6] Radaj, D., Lehrke, H.P., and Greuling, S., “Theoretical Fatigue Effective Notch Stresses at Spot Welds”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 24, No. 5, pp. 293-308, (2001).
 
[7] Smith, E., “The Mode III Elastic Stress Distribution Near the Root of (a) an Intrusion-Type Notch and (b) a Key-hole Notch”, International Journal of Engineering Science, Vol. 44, No. 5-6, pp. 340-344, (2006).
 
[8] Kullmer, G., and Richard, H.A., “Influence of the Root Radius of Crack-like Notches on the Fracture Load of Brittle Components”, Archive of Applied Mechanics, Vol. 76, No. 11-12, pp. 711-723, (2006).
 
[9] Creager, M., and Paris, P.C., “Elastic Field Equations for Blunt Cracks with Reference to Stress Corrosion Cracking”, International Journal of Fracture Mechanics, Vol. 3, No. 4, pp. 247–252, (1967).
 
[10] Pook, L.P., “Finite Element Analysis of Corner Point Displacements and Stress Intensity Factors for Narrow Notches in Square Sheets and Plates”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 23, No. 12, pp. 979–992, (2000).
 
[11] Larsson, S.G., and Carlsson, A.J., “Influence of Non-singular Stress Terms and Specimen Geometry on Small-scale Yielding at Crack-tips in Elastic–plastic Materials”, Journal of the Mechanics and Physics of Solids, Vol. 21, No. 4, pp. 263–277, (1973).
 
[12] Rice, J.R., “Limitations to the Small Scale Yielding Approximation for Crack Tip Plasticity”, Journal of the Mechanics and Physics of Solids, Vol. 22, No. 1, pp. 17–26, (1974).
 
[13] Cotterell, B., “Notes on the Paths and Stability of Cracks”, International Journal of Fracture, Vol. 2, No. 3, pp. 526-533, (1966).
 
[14] Melin, S., “The Influence of the T-stress on the Directional Stability of Cracks”, International Journal of Fracture, Vol. 114, No. 3, pp. 259–265, (2002).
 
[15] Fett, T., and Munz, D., “T-stress and Crack Path Stability of DCDC Specimens”, International Journal of Fracture, Vol. 124, No. 1-2, pp. L165–L170, (2003).
 
[16] Smith, D.J., Ayatollahi, M.R., and Pavier, M.J., “The Role of T-stress in Brittle Fracture for Linear Elastic Materials under Mixed-mode Loading”, Fatigue and Fracture of Engineering Materials and Structures, Vol. 24, No. 2, pp. 137–150, (2001).
 
[17] Ayatollahi, M.R., Pavier, M.J., and Smith, D.J., “Mode I Cracks Subjected to Large T-stresses”, International Journal of Fracture, Vol. 117, No. 2, pp. 159–174, (2002).
 
[18] Karihaloo, B.L., “Size Effect in Shallow and Deep Notched Quasi-brittle Structures”, International Journal of Fracture, Vol. 95, pp. 379–390, (1999).
 
[19] Kardomateas, G.A., Carlson, R.L., Soediono, A.H., and Schrage, D.P., “Near-tip Stress and Strain Fields for Short Elastic Cracks”, International Journal of Fracture, Vol. 62, No. 3, pp. 219–232, (1993).
 
[20] Kim, J.K., and Cho, S.B., “Effect of Second Non-singular Term of Mode I Near the Tip of a V-notched Crack”, Fatigue and Fracture of Engineering Materials & Structures, Vol. 32, No. 4, pp. 346–356, (2009).
 
[21] Ayatollahi, M.R., and Nejati, M., “An Over-deterministic Method for Calculation of Coefficients of Crack Tip Asymptotic Field from Finite Element Analysis”, Fatigue and Fracture of Engineering Materials and Structures, Vol. 34, No. 3, pp. 159–176, (2011).
 
[22] Ayatollahi, M.R., and Nejati, M., “Determination of NSIFs and Coefficients of Higher Order Terms for Sharp Notches using Finite Element Method”, International Journal of Mechanical Sciences, Vol. 53, No. 3, pp. 164–177, (2011).
 
[23] Williams, M.L., “Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension”, Journal of Applied Mechanics, Vol. 19, No. 4, pp. 526-528, (1952).